Compressed sensing or compressive sampling (CS) is an emerging signal processing technique that asserts that certain signals can be recovered faithfully from far fewer number of samples or measurements. CS relies on the underlying structure of the signal which is expressed in terms of its ‘sparsity’ and the ‘incoherence’ which is related to the sampling scheme (see for example “An Introduction to compressive sampling”, E. J. Candès et al., IEEE Signal Processing Magazine, vol. 25, pp 21-30, March 2008).
Known state-of-the-art biosignal acquisition systems using, for example, the techniques described in “Compressed Sensing System Considerations for ECG and EMG Wireless Biosensors”, A. M. R. Dixon et al., IEEE Transactions on Biomedical Circuits and Systems, vol. 6, No. 2, April 2012, require, for the reconstruction of an approximation of the original sampled signals, long reconstruction windows of samples N to induce sufficient signal sparsity and optimize reconstruction quality (reduce reconstruction error). On the other hand, the processing of long reconstruction windows of samples N increases latency and requires significant computational complexity, e.g. up to O(N3), since the computational complexity of the reconstruction depends on the reconstruction window sample size N, which makes current techniques inadequate for embedded applications.
Therefore, there exists a link between the CS reconstruction window sample length, signal reconstruction quality, and processing complexity. This trade-off is also apparent from the paper “An ultra low power pulse oximeter sensor based on compressed sensing”, P. K. Baheti et al., Body Sensor Networks 2009, pp 144-148, Berkeley, USA 2009.
Improvements to current state of the art compressed sensing systems and methods are therefore desired.